Foundations of the Non-Linear Mechanics of Continua

Foundations of the Non-Linear Mechanics of Continua

International Series of Monographs in Interdisciplinary and Advanced Topics in Science and Engineering, Vol. 1

1st Edition - January 1, 1966

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  • Author: L. I. Sedov
  • eBook ISBN: 9781483222608

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Description

International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3. This volume is suitable for persons who intend to do research on the development of the theory of dynamics and thermodynamics or solve specific theoretical problems on the motion of a continuous medium with finite deformations.

Table of Contents


  • Editor's Preface

    Foreword

    Introduction

    Chapter I. Outline of Tensor Calculus

    1. Curvilinear Systems of Coordinates

    2. Transformation of Coordinates

    3. The Concept of a Tensor and the Fundamentals of the Algebra of Tensors

    4. Tensors of Second Rank

    5. Tensor Functions

    6. Functions of Several Tensors

    7. Tensor Potential Functions

    8. Differentiation of Tensors with Respect to Space Coordinates

    9. The Riemann-Christoffel Tensor

    10. Differentiation of Tensors with Respect to Parameters

    Chapter II. Kinematics of a Deformable Medium

    1. General Features of Continuous Deformations

    2. Affine Deformations

    3. Regular Finite Displacements of a Continuum

    4. The Deformation Tensors

    5. The Vector of Rotation of the Axes of Deformation

    6. Kinematic Tensors Characterizing a Deformation

    7. The Differentiation of Non-Linear Tensor Functions

    8. The Conditions of Compatibility

    Chapter III. Dynamic and Thermodynamic Exposition

    1. Physical Considerations

    2. The Concept of a Material Continuum

    3. The Equations of Continuity

    4. Dynamical Equations

    5. The Theorem of Kinetic Energy and the Work of the Internal Surface Forces

    6. Thermodynamic Systems and Cycles. The Equation of Conservation of Energy and the Concept of the Internal Energy of a System

    7. The Basic Concepts and Consequences of the Second Law of Thermodynamics

    8. Ideal Liquids and Gases

    9. The Simplest Ideal Processes

    10. Special Examples of Ideal Compressible Media

    11. The Equations of Motion of Gas Mixtures with Physico-Chemical Interaction Between the Components

    12. Viscous Liquids and Gases

    13. The Turbulent Flow of Continuous Media

    14. The Model of an Elastic Body

    15. Thermoelastic Isotropic Media

    16. Some Remarks on Mechanical Models for Irreversible Processes

    17. Plastic, Elastic and Total Deformations

    18. The Elastic Range and the Loading Surface

    19. The Basic Laws in the Theories of Plastic Bodies

    20. Models of Plastic Media for which the Loading Surface Possesses Singular Points

    References

    Index

Product details

  • No. of pages: 268
  • Language: English
  • Copyright: © Pergamon 1966
  • Published: January 1, 1966
  • Imprint: Pergamon
  • eBook ISBN: 9781483222608

About the Author

L. I. Sedov

About the Editor

Simon Ostrach

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